We are given the equation y = 3x - 6
The slope-intercept form of a line is y = mx + b where m is the slope and b is the y-intercept.
The b value in this equation is -6, thus the y-intercept is -6.
Let me know if you need any clarifications, thanks!
x varies directly as y, when x=4,y=3. find Y when x=5
Answer:
Y =4
Step-by-step explanation:
Hope it helps
1. find x and y 2. find the measure of each side of LMN
Answer:
X= 3
Y= 18
Each side of the triangle= 10 units
Step-by-step explanation:
LMN is equilateral so
LM = MN
3x+1= 4x-2
3x-4x = -2-1
-x = -3
X= 3
MP is the perpendicular bisector of line LN
so definitely angle lpm =90.
And lpm = 5y = 90
5y = 90
Y= 90/5
Y = 18°
For the side of the triangle
3x+1
But x= 3
3(3)+1
9+1
10
Each side of the triangle= 10 units
The linear combination method is applied to a system of equations as shown. 4(.25x + .5y = 3.75) → x + 2y = 15 (4x – 8y = 12) → x – 2y = 3 2x = 18
Answer:
x+2y=12-------(1)
x-2y=3---------(2)
Adding equations 1 and 2
we get
2x=18
x=9
Equation 1
9+2y=15
2y=15-9
2y=6
y=3
The solution of the given system is x=9, y=3
Step-by-step explanation
A city's population is currently 50,000. If the population doubles every 70 years, what will the population be 280 years from now?
Answer:
200,000
Step-by-step explanation:
The current population: 50,000
Doubling time:70
Population after 280 years=?
280/70=4
50,000*4=200,000
Hope this helps ;) ❤❤❤
Answer: 800,000
Step-by-step explanation: 50,000x2=100,000. That is after 70 years. 100,000x2=200,000. This is after 140 years. 200,000x2=400,000. This is after 210 years. 400,000x2=800,000. This is after 280 years.
Which equation is graphed in the figure? A. 7y = 5x + 14 B. 7y = -5x + 14 C. 5y = -7x + 10 D. 5y = 7x + 10
Answer:
The answer is D. You can confirm this from the graph down below
Step-by-step explanation:
2| x-3| - 5 = 7 Helpp
Answer:
x = {9, -3}
Step-by-step explanation:
2| x-3| - 5 = 72| x-3| = 12| x-3| = 6x - 3 = ± 6 ⇒ x= 3+ 6= 9⇒ x= 3 - 6= -3Or it can be shown as:
x= {9, -3}The following are the weekly amounts of welfare payments made by the federal government to a sample of six families: $139, $136, $130, $136, $147, and $136. What is the range
Answer:
$17
Step-by-step explanation:
data:
$139 $136 $130 $136 $147 $136In statistics, the range is the difference between the highest value and the lowest value of the data set.
Highest value = $147
Lowest value = $130
Range = $17
can someone help me with these ones :(? (with full process)
1.) (3,2) and (4,j),m=1
2). (5,0) and (1,k),m=1/2
3).(x, 2) and (3, -4), m = 2
4). (12, -4) y (r, 2), m = -1/2
Answer:
The answers for:
j = 3k = -2x = 6r = 0Step-by-step explanation:
In order to find the value of expression, you have to apply gradient formula :
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
So for Question 1,
[tex]let \: (3,2) \: be \: (x1,y1) \\ let \: (4,j) \: be \: (x2,y2) \\ let \: m = 1[/tex]
[tex] \frac{j - 2}{4 - 3} = 1[/tex]
[tex] \frac{j - 2}{1} = 1[/tex]
[tex]j - 2 = 1[/tex]
[tex]j = 1 + 2 = 3[/tex]
Question 2,
[tex]let \: (5,0) \: be \: (x1,y1) \\ let \: (1,k) \: be \: (x2,y2) \\ let \: m = \frac{1}{2} [/tex]
[tex] \frac{k - 0}{1 - 5} = \frac{1}{2} [/tex]
[tex] \frac{k}{ - 4} = \frac{1}{2} [/tex]
[tex]k = \frac{1}{2} \times - 4 = - 2[/tex]
Question 3,
[tex]let \: (x,2) \: be \: (x1,y1) \\ let \: (3, - 4) \: be \: (x2,y2) \\ let \: m = 2[/tex]
[tex] \frac{ - 4 - 2}{3 - x} = 2[/tex]
[tex] \frac{ - 6}{3 - x } = 2[/tex]
[tex] - 6 = 2(3 - x)[/tex]
[tex] - 6 = 6 - 2x[/tex]
[tex] - 6 - 6 = - 2x[/tex]
[tex] - 2x = - 12[/tex]
[tex]x = - 12 \div - 2 = 6[/tex]
Question 4,
[tex]let \: (12, - 4) \: be \: (x1,y1) \\ let \: (r,2) \: be \: (x2,y2) \\ let \: m = - \frac{1}{2} [/tex]
[tex] \frac{2 - ( - 4)}{r - 12} = - \frac{1}{2} [/tex]
[tex] \frac{6}{r - 12} = - \frac{1}{2} [/tex]
[tex] - 1(r - 12) = 2(6)[/tex]
[tex] - r + 12 = 12[/tex]
[tex]r = (12 - 12) \div - 1 = 0[/tex]
HELP PLEASE The graph of an exponential function of the form y = f(x) = ax passes through the points ______ and _______. The graph lies_____ the x-axis.
Answer:
1). (0, 1)
2). (1, a)
3). Above
Step-by-step explanation:
This question is not complete; here is the complete question.
The graph of an exponential function of the form y = f(x) = [tex]a^{x}[/tex] passes through the points 1). and 2). . The graph lies 3). x-axis.
1). (0.a), (0,1), (0,2), (0,-1)
2). (1,0), (1,1), (1,a), (1,-2)
3). (above), (below), (on the)
Given exponential function is f(x) = [tex]a^{x}[/tex]
1). For x = 0,
f(0) = [tex]a^{0}[/tex] = 1
Therefore, the given exponential function passes through a point (0, 1).
2). For x = 1,
f(1) = [tex]a^{1}[/tex]
f(1) = a
Therefore, graph of the exponential function passes through (1, a)
3).For y = 0
0 = [tex]a^{x}[/tex]
But for any value of 'x', f(x) will never be zero. Therefore, there is no x-intercept.
The graph lies above the x-axis.
Suppose that f and g are functions that are differentiable at x = 1 and that f(1) = 2, f '(1) = −1, g(1) = −2, and g'(1) = 3. Find h'(1). h(x) = (x2 + 8)g(x)
Answer:
[tex]h'(1) = 23[/tex]
Step-by-step explanation:
Let be [tex]h(x) = (x^{2}+8)\cdot g(x)[/tex], where [tex]r(x) = x^{2} + 8[/tex]. If both [tex]r(x)[/tex] and [tex]g(x)[/tex] are differentiable, then both are also continuous for all x. The derivative for the product of functions is obtained:
[tex]h'(x) = r'(x) \cdot g(x) + r(x) \cdot g'(x)[/tex]
[tex]r'(x) = 2\cdot x[/tex]
[tex]h'(x) = 2\cdot x \cdot g(x) + (x^{2}+8)\cdot g'(x)[/tex]
Given that [tex]x = 1[/tex], [tex]g (1) = -2[/tex] and [tex]g'(1) = 3[/tex], the derivative of [tex]h(x)[/tex] evaluated in [tex]x = 1[/tex] is:
[tex]h'(1) = 2\cdot (1) \cdot (-2) + (1^{2}+8)\cdot (3)[/tex]
[tex]h'(1) = 23[/tex]
Rafael is putting money into a savings account. He starts with $350 in the savings account, and each week he adds $60. Let S represent the total amount of money in the savings account (in dollars), and let W represent the number of weeks Rafael has been adding money. Write an equation relating S to W. Then use this equation to find the total amount of money in the savings account after 19 weeks.
Answer:
Equation: S(W) = 60W + 350
After 19 weeks, total accumulated = S(19) = 1490
Step-by-step explanation:
The interest rate is not indicated, so cannot take that into account.
Each week, he adds 60$, with initial value of 350$
So the equation is
S(W) = 60W + 350
for W = 19,
S = 60*19 + 350
S(19) = 1490
Answer:
$1490
Step-by-step explanation:
Write the slip-intercept form of the equation of the line described
- through: (4,1), parallel to y = 5/6x - 3
- through: (3,3), perp. to y= -3/8x + 2
Answer:
1) y=⅚x -2⅓
2) y=8/3x -5
Step-by-step explanation:
Point-slope form:
y=mx+c, where m is the gradient and c is the y-intercept.
Parallel lines have the same gradient.
Gradient of given line= [tex] \frac{5}{6} [/tex]
Thus, m=⅚
Susbt. m=⅚ into the equation,
y= ⅚x +c
Since the line passes through the point (4, 1), (4, 1) must satisfy the equation. Thus, substitute (4, 1) into the equation to find c.
When x=4, y=1,
1= ⅚(4) +c
[tex]1 = \frac{20}{6} + c \\ c = 1 - \frac{20}{6} \\ c = 1 - 3 \frac{1}{3} \\ c = - 2 \frac{1}{3} [/tex]
Thus the equation of the line is [tex]y = \frac{5}{6} x - 2 \frac{1}{3} [/tex].
The gradients of perpendicular lines= -1.
Gradient of given line= -⅜
-⅜(gradient of line)= -1
gradient of line
= -1 ÷ (-⅜)
= -1 ×(-8/3)
= [tex] \frac{8}{3} [/tex]
[tex]y = \frac{8}{3} x + c[/tex]
When x=3, y=3,
[tex]3 = \frac{8}{3} (3) + c \\ 3 = 8 + c \\ c = 3 - 8 \\ c = - 5[/tex]
Thus the equation of the line is [tex]y = \frac{8}{3} x - 5[/tex].
A cable company must provide service for 6 houses in a particular neighborhood. They would like to wire the neighborhood in a way to minimize the wiring costs (or distance). What is the minimal length of the network required to span the entire neighborhood? House Distances (yards) 1 to 2 250 1 to 3 400 1 to 4 300 2 to 3 400 2 to 4 400 2 to 5 400 3 to 5 350 3 to 6 450 4 to 5 300 4 to 6 350
Answer:
1650 yards
Step-by-step explanation:
Here, we have to find the minimal spanning tree required to span the neighborhood.
We start from house 1. The minimum distance from house 1 to house 2 is 250 yards. Now from 2, we can go to house 3,4 or 5 all having the equal distances of 400 yard from house 2. So we go to from house 2 to house 3. Now from 3, we go to house 5 which is at a minimum distance of 350 yards. Now from house 5 we go to house 4 with 300 yards and then from house 4 we go to house 6 which is at 350 yards from 4.
Thus the network is complete and the total distance covered is
= 250 + 400 + 350 + 300 + 350
= 1650 yards
This is the minimum distance by which the neighborhood can be wired.
And the tree is
[tex]$1\rightarrow2\rightarrow3\rightarrow5\rightarrow4\rightarrow6$[/tex]
find the coordinates of Q' after a reflection across parallel lines; first across the line y= -2 and then across the x-axis
Answer: new Q = (-4, 5)
Step-by-step explanation:
Given: Q = (-4, 1)
Reflected across y = -2:
Q is 3 units above y = -2 so a reflection is 3 units below y = -2 --> Q' = (-4, -5)
Reflected across x-axis:
Q' is 5 units below x-axis so a reflection is 5 units above x-axis --> Q'' = (-4, 5)
What is the value of the fourth term in a geometric sequence for which a1 =
30 and r= 1/2
Answer:
3¾
Step-by-step explanation:
Geometric sequence also known as geometric progression, can be said to be a sequence with a constant ratio between the terms.
Formula for geometric sequence:
[tex] a^n = a ( n-1 ) * r [/tex]
Given:
First term, a1 = 30
ratio, r = ½
Required:
Find the fourth term
Where, the first term, a¹ = 30
Second term: a² = 30 * ½ = 15
Third term: a³ = 15 * ½ = 7.5
Fourth term: a⁴ = 7.5 * ½ = 3.75 = 3¾
Therfore the fourth term of the geometric sequence is 3¾
What is the range of the function (-1,2) (3,6) (5,8)
Answer:
Range { 2,6,8}
Step-by-step explanation:
The domain is the input and the range is the output
Range { 2,6,8}
Answer:
2, 6, 8
Step-by-step explanation:
The range is the possible values of y, (x, y). So in this case, y could be 2, 6, or 8.
If cot(x)=2/3, what is The value of csc(x)
Answer:
Step-by-step explanation:
cot (x)=2/3
we know csc^2(x)-cot^2(x)=1
csc^2(x)=1+cot^2(x)=1+4/9=13/9
csc (x)=±√13/3
By looking at the plots, Beth says that the two means are about 5 years apart. Which is true about Beth's statement?
She is correct because the medians are 10 years apart,
which means the means are half of that, or 5 years
apart
O She is correct because the maximum ages of the
pennies in each set are 5 years apart.
O She is not correct because the means are both equal to
02
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36
12
O She may not be correct because means cannot be
determined from the box plots.
4x ≤12 dimplify solve for x
Answer:
x<3
Step-by-step explanation:
Answer:
[tex]\boxed{x\leq 3}[/tex]
Step-by-step explanation:
[tex]4x \leq 12[/tex]
[tex]\sf Divide \ both \ parts \ by \ 4.[/tex]
[tex]\displaystyle \frac{4x}{4} \leq \frac{12}{4}[/tex]
[tex]x\leq 3[/tex]
In a large university, 20% of the students are business majors. A random sample of 100 students is selected, and their majors are recorded. a) Compute the standard error of the proportion. b) What is the probability that the sample contains at least 12 business majors
Answer:
a. 0.04
b. 0.9772
Step-by-step explanation:
Please check attachment for complete solution and step by step explanation
"Radon: The Problem No One Wants to Face" is the title of an article appearing in Consumer Reports. Radon is a gas emitted from the ground that can collect in houses and buildings. At certain levels it can cause lung cancer. Radon concentrations are measured in picocuries per liter (pCi/L). A radon level of 4 pCi/L is considered "acceptable." Radon levels in a house vary from week to week. In one house, a sample of 8 weeks had the following readings for radon level (in pCi/L). 1.92.45.75.51.98.23.96.9 (a) Find the mean, median, and mode. (Round your answers to two decimal places.) mean 4.55 median 4.7 mode 1.9 (b) Find the sample standard deviation, coefficient of variation, and range. (Round your answers to two decimal places.) s CV % range (c) Based on the data, would you recommend radon mitigation in this house
Answer:
a) Mean = 4.55
Median = 4.7
Mode = 1.9
b) S = 2.3952
CV = 52.64 %
Range = 6.3
c) Yes, since the average and median values are both over "acceptable" ranges.
Step-by-step explanation:
Explanation is provided in the attached document.
PLEASE HELP WILL GIVE EVERYTHING Amare wants to ride a Ferris wheel that sits four meters above the ground and has a diameter of 50 meters. It takes six minutes to do three revolutions on the Ferris wheel. Complete the function, h(t), which models Amare's height above the ground, in meters, as a function of time, t, in minutes. Assume he enters the ride at the low point when t = 0.
Answer:
[tex]h(t)=-25\cos(\pi t)+29[/tex]
Step-by-step explanation:
First thing to understand is that we will be producing a sine or cosine function to solve this one. I'll use a cosine function for the sake of the problem, since it's most easily represented by a cosine wave flipped over. If you're interested in seeing a visualization of how a circle's height converts to one of these waves, you may find the Better Explained article Intuitive Understanding of Sine Waves helpful.
Now let's get started on the problem. Cosine functions generally take the form
[tex]y=a\cos(b(x-c))+d[/tex]
Where:
[tex]|a|[/tex] is the amplitude
[tex]\frac{2\pi}{b}[/tex] is the period, or the time it takes to go one full rotation around the circle (ferris wheel)
[tex]c[/tex] is the horizontal displacement
[tex]d[/tex] is the vertical shift
Step one, find the period of the function. To do this, we know that it takes six minutes to do three revolutions on the ferris wheel, so it takes 2 minutes to do one full revolution. Now, let's find [tex]b[/tex] to put into our function:
[tex]\frac{2\pi}{b}=2[/tex]
[tex]2\pi=2b[/tex]
[tex]\pi=b[/tex]
I skipped some of the basic algebra to shorten the solution, but we have found our b. Next, we'll get the amplitude of the wave by using the maximum and minimum height of the wheel. Remember, it's 4 meters at its lowest point, meaning its highest point is 54 meters in the air rather than 50. Using the formula for amplitude:
[tex]\frac{\max-\min}{2}[/tex]
[tex]\frac{54-4}{2}[/tex]
[tex]\frac{50}{2}=25=a[/tex]
Our vertical transformation is given by [tex]\min+a[/tex] or [tex]\max-a[/tex], which is the height of the center of the ferris wheel, [tex]4+25=29=d[/tex]
Because cosine starts at the minimum, [tex]c=0[/tex].
The last thing to point out is that a cosine wave starts at its maximum. For that reason, we need to flip the entire function by making the amplitude negative in our final equation. Therefore our equation ends up being:
[tex]h(t)=-25\cos(\pi t)+29[/tex]
A train is booked to do the run between two places 55 km apart,in 1 hr 20 min. if it travels for the first 30 km at 36km per hour, at what speed must it travel for the rest of the distance in order to complete the journey in time
Answer:
The train must travel at 50 km/hr to make it on time.
Step-by-step explanation:
distance to be covered = 55 km
time to cover this distance = 1 hr 20 min
1 hr 20 min = 1.33 hrs (20 min = 20/60 hrs = 0.33 hrs)
The train travels the first 30 km distance at a speed of 36 km/hr
and we know that time taken = distance/speed
therefore the time taken to run this 30 km will be
time = 30/36 = 0.83 hr
The train still has 55 - 30 = 25 km to cover,
and the time left is 1.33 - 0.83 = 0.5 hrs left
to make it on time, the train must travel at
speed = distance/time = 25/0.5 = 50 km/hr
The alpha level that a researcher sets at the beginning of the experiment is the level to which he wishes to limit the probability of making the error of____________
Answer:
not rejecting the null hypothesis when it is false.
Step-by-step explanation:
Significance level or alpha level is the probability of rejecting the null hypothesis when null hypothesis is true. It is considered as a probability of making a wrong decision. It is a statistical test which determines probability of type I error. If the obtained probability is equal of less than critical probability value then reject the null hypothesis.
For making the error, it should not reject the null hypothesis at the time when it should be false.
What is alpha level?It is the level where the probability of rejecting the null hypothesis at the time when the null hypothesis should be true. It is relevant for making the incorrect decision. Also, it is the statistical test that measured the probability of type 1 error.
Therefore, For making the error, it should not reject the null hypothesis at the time when it should be false.
Learn more about error here: https://brainly.com/question/18831983
If w'(t) is the rate of growth of a child in pounds per year, what does 7 w'(t)dt 4 represent? The change in the child's weight (in pounds) between the ages of 4 and 7. The change in the child's age (in years) between the ages of 4 and 7. The child's weight at age 7. The child's weight at age 4. The child's initial weight at birth.
Complete Question
If w'(t) is the rate of growth of a child in pounds per year, what does
[tex]\int\limits^{7}_{4} {w'(t)} \, dt[/tex] represent?
a) The change in the child's weight (in pounds) between the ages of 4 and 7.
b) The change in the child's age (in years) between the ages of 4 and 7.
c) The child's weight at age 7.
d) The child's weight at age 4. The child's initial weight at birth.
Answer:
The correct option is option a
Step-by-step explanation:
From the question we are told that
[tex]w'(t)[/tex] represents the rate of growth of a child in [tex]\frac{pounds}{year}[/tex]
So [tex]{w'(t)} \, dt[/tex] will be in [tex]pounds[/tex]
Which then mean that this [tex]\int\limits^{7}_{4} {w'(t)} \, dt[/tex] the change in the weight of the child between the ages of [tex]4 \to 7[/tex] years
PLEASE HELP!! Write the proportion. 120 feet is to 150 feet as 8 feet is to 10 feet. (18 points!!)
Answer:
4 : 5
Step-by-step explanation:
you can divide 120 and 150 by 30 and 8 and 10 by 2.
120/30 = 4
150/30 = 5
8/2 = 4
10/2=5
Answer: 4:5
Step-by-step explanation:
Please help. I’ll mark you as brainliest if correct!
Answer:
Since we are talking annual interest and, I assume a time period of 1 year:
The interest earned is the sum of the interest earned on the two loans separately
Let x = amount loaned at 14%
18,500-x = amount loaned at 12%
I = prt
p = x and 18500-x
r = 0.14 and 0.12
t = 1
2390 = 0.14x + 0.1(18500-x)
2390 = .14x + 1850 - 0.1x
x = 13500
x = $13,500 loaned at 14%
18500-x = $5,000 loaned at 12%
Answer:
$8,500 was loaned at 14%, and
$10,000 was loaned at 12%.
Step-by-step explanation:
Total loan: $18,500.
Part at 14%
Part at 12%
Let the part at 14% = x.
Let the part at 12% = y.
Equation of amount of loan:
x + y = 18500
x amount at 14% earns 14% of x = 0.14x interest.
y amount at 12% earns 12% of y = 0.12y interest.
Equation of interest charged:
0.14x + 0.12y = 2390
We have a system of equations.
x + y = 18500
0.14x + 0.12y = 2390
Multiply both sides of the first equation by -0.12. Write the second equation below it, and add the equations.
-0.12x - 0.12y = -2220
(+) 0.14x + 0.12x = 2390
-------------------------------------
0.02x = 170
x = 170/0.02
x = 8500
x + y = 18,500
8500 + y = 18,500
y = 10,000
Answer:
$8,500 was loaned at 14%, and
$10,000 was loaned at 12%.
13. How long will a man take to cover
a distance of 7 kilometres by
walking 4 kilometres per hour?
(a) 1 hr. 35mins.
b) 1hr. 45mins
(c) Less than 1hr
(d) Exactly 1 hr.
(e) More than 2hrs
7km/ 4km per hour = 1 3/4 hours
3/4 hour = 45 minutes
Total time = 1 hour and 45 minutes.
what is the length of a rectangle with width 12 inches and an area of 66 inches^2
Answer:
The length is 5.5 inches
Step-by-step explanation:
The area of a rectangle is
A = lw
66 = l * 12
Divide each side by 12
66/12 = l
5.5 = l
The length is 5.5 inches
Answer:
5.5 inches
Step-by-step explanation:
Length times width is the area so
12*width =66
same as
66/12=5.5 inches
Ask more questions in the comments if you are still confused.
Bryan invests $500 in an account earning 3.5% interest that compounds annually. If he makes no additional deposits or withdraws, how much will be in the account:
After 10 years?
After 15 years?
After 20 years?
Answer:
$705.30, $837.67, $994.89 Respectively
Step-by-step explanation:
Given
P= $500
r= 3.5%= 3.5/100= 0.035
Applying the compound interest formula we have
[tex]A= P(1+r)^t[/tex]
where
A = final amount
P = initial principal balance
r = interest rate
t = number of time periods elapsed
1. for t= 10 years[tex]A= 500(1+0.035)^1^0\\\ A= 500(1.035)^1^0\\\\ A= 500*1.410598\\\ A=705.299[/tex]
A= $705.30
2. for t= 15 years[tex]A= 500(1+0.035)^1^5\\\ A= 500(1.035)^15\\\\ A= 500*1.67534\\\ A=837.67[/tex]
A= $837.67
3. for t= 20 years[tex]A= 500(1+0.035)^2^0\\\ A= 500(1.035)^2^0\\\\ A= 500*1.98978\\\ A=994.89[/tex]A= $994.89